Benford's law & anomalies (numbers 1-3)

[Trinitiet]

Hi,

I've been studying Benford's law lately. The problem I've been getting, however, is that the anomalies compared to the theoretical values are quite big.

My last investigation was about nuclear levels between 1 MeV and -I think- 1 000 000 MeV. I got this information on this website: http://cdfe.sinp.msu.ru/services/ensdfr.html.

Using this website, I managed to get ~133 000 nuclear levels, which should be enough to get rid of big statistical fluctuations.

My measurement:
http://desmond.imageshack.us/Himg4/scaled.php?server=4&filename=graphbenfordnuclearleve.png&res=medium
The circles show the theoretical values, the triangles show what I measured.

As one can see, I really have the right trend for numbers 4 to 9. I am however worried about the fluctuations in numbers 1 to 3, they're really too big (for my intuition) to be -just- statistical fluctuations.

I studied the Wikipedia page and I cannot find any argument why Benford's law would not apply on my set of data. I wonder if anyone on this forum knows why my data shows this big of anomalies vs. Benford's law?

Thanks,
Trinitiet.

P.S. My code was written in R. I tested the code multiple times on small sets of data so I'm quite confident there's nothing wrong with my results.

 

[mmwave]

Hi Trinitiet,

Thank you for sharing your findings on Benford's law with us. It's always interesting to see how this law applies in different fields, such as nuclear levels in your case.

First of all, I would like to commend you for your thoroughness in gathering a large dataset and testing your code multiple times. This shows that you have taken the necessary steps to ensure the accuracy of your results.

I took a look at your graph and I can see that there are indeed some discrepancies between the theoretical and measured values, particularly in the numbers 1 to 3. While I cannot say for certain why this is happening, I have a few suggestions that may help in understanding these anomalies.

Firstly, it is possible that there may be some outliers or errors in the data that are causing these discrepancies. I would recommend checking your dataset for any unusual or incorrect values that may be skewing the results. It may also be helpful to remove any extreme values and see if that affects the distribution of your data.

Secondly, it is worth considering the possibility that Benford's law may not apply perfectly in this particular case. While this law is generally observed in many real-world datasets, there are always exceptions and variations. It is possible that the nature of nuclear levels may not follow the same distribution as other datasets, which could explain the deviations from Benford's law.

Lastly, it may be helpful to compare your results with other studies or datasets on nuclear levels to see if they also show similar discrepancies. This could provide further insight into the applicability of Benford's law in this field.

I hope these suggestions are helpful in understanding the anomalies in your data. Keep exploring and questioning, that's what science is all about. Good luck with your research!